Question #1 a. What is formula for the variance of OLS estimates of the intercept and slope coefficients. b. Using the formulas above, explain how each if the following factor affects the variance of OLS estimates of the intercept and slope coefficients. i. the error variance ii. the size of the sample of pbservations iii. the total sample variation of the X values iv. the total sample variation of the Y values Question #2 An Econometrics student is using data for a sample of 27 Belizean firms to investigate the relationship between annual profits (Y), measured in millions of BZS per year, and annual sales revenues (X), measured in billions of BZS per year. The population regression equation of interest is: i=1+2Xi+Ui Preliminary analysis of the sample data produces the following sample information: i=1Yi=12,767iXi=570.175 i=1i2=11,890,057 i=1Xi3=19,058.49 i=1Ui2=3,468,497.03 jyx,129,363. xi=7,017,77 where yi=yiY and xi=Xix for i=1,2,3n. Use the above sample information to answer all the following questions: 1. Canspate the OLLS estinantes of the intercept and slupe coefficicate. 2. Provide an iaterpetation of the slope corficiest estienate: 3. Conspete the value of R2 and pecwisle an interpertation of this value 4. Calculate the extimated varinames of p1 and 32. H1=X2+0 at the 5%. xignificance level. State the decivios rule yod teal, asd the perfotmed the test at the 17 signiticazce berelt 6. Comagute the two-sided 25K confidence interinl foe the sloje coefficirat 32. 7. Perform a test of the mill hypothers He:d210 acninst the ahernative lajwilvois H1:H2>10 at the 5% siguificabce level. State the derision rule got ase, and the inference yog would draw frota the test. World you draw the seman imserence af your perfotaned the tost at the 1Ke sipniticnace kvelt 8. Perform a test of the null hypothesd of no regrexion at the 5% sienititance level. Question #1 a. What is formula for the variance of OLS estimates of the intercept and slope coefficients. b. Using the formulas above, explain how each if the following factor affects the variance of OLS estimates of the intercept and slope coefficients. i. the error variance ii. the size of the sample of pbservations iii. the total sample variation of the X values iv. the total sample variation of the Y values Question #2 An Econometrics student is using data for a sample of 27 Belizean firms to investigate the relationship between annual profits (Y), measured in millions of BZS per year, and annual sales revenues (X), measured in billions of BZS per year. The population regression equation of interest is: i=1+2Xi+Ui Preliminary analysis of the sample data produces the following sample information: i=1Yi=12,767iXi=570.175 i=1i2=11,890,057 i=1Xi3=19,058.49 i=1Ui2=3,468,497.03 jyx,129,363. xi=7,017,77 where yi=yiY and xi=Xix for i=1,2,3n. Use the above sample information to answer all the following questions: 1. Canspate the OLLS estinantes of the intercept and slupe coefficicate. 2. Provide an iaterpetation of the slope corficiest estienate: 3. Conspete the value of R2 and pecwisle an interpertation of this value 4. Calculate the extimated varinames of p1 and 32. H1=X2+0 at the 5%. xignificance level. State the decivios rule yod teal, asd the perfotmed the test at the 17 signiticazce berelt 6. Comagute the two-sided 25K confidence interinl foe the sloje coefficirat 32. 7. Perform a test of the mill hypothers He:d210 acninst the ahernative lajwilvois H1:H2>10 at the 5% siguificabce level. State the derision rule got ase, and the inference yog would draw frota the test. World you draw the seman imserence af your perfotaned the tost at the 1Ke sipniticnace kvelt 8. Perform a test of the null hypothesd of no regrexion at the 5% sienititance level
